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<meta name="description" content="概述 快速排序与归并排序一样也是基于分治算法的排序算法.所以它的实现方法也与其他的分治算法一样,需要进行分解子任务,处理子任务,归并子任务这些步骤. 但快速排序与归并排序不同,它是一种原地排序算法(不需要额外的辅助数组),且快速排序不使用中间值来分解任务,而是使用划分函数. 算法过程   从数组中挑选出一个值,作为基准值 k.   重新排序序列,将所有小于k的值放到k前面,所有大于k的值放到k后面">
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<meta property="og:description" content="概述 快速排序与归并排序一样也是基于分治算法的排序算法.所以它的实现方法也与其他的分治算法一样,需要进行分解子任务,处理子任务,归并子任务这些步骤. 但快速排序与归并排序不同,它是一种原地排序算法(不需要额外的辅助数组),且快速排序不使用中间值来分解任务,而是使用划分函数. 算法过程   从数组中挑选出一个值,作为基准值 k.   重新排序序列,将所有小于k的值放到k前面,所有大于k的值放到k后面">
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          深入浅出排序算法(3)-快速排序
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        <h3 id="概述"><a href="#概述" class="headerlink" title="概述"></a>概述</h3><hr>
<p><code>快速排序</code>与<code>归并排序</code>一样也是基于分治算法的排序算法.所以它的实现方法也与其他的分治算法一样,需要进行分解子任务,处理子任务,归并子任务这些步骤.</p>
<p>但<code>快速排序</code>与<code>归并排序</code>不同,它是一种<code>原地排序</code>算法(不需要额外的辅助数组),且<code>快速排序</code>不使用中间值来分解任务,而是使用<code>划分函数</code>.</p>
<h3 id="算法过程"><a href="#算法过程" class="headerlink" title="算法过程"></a>算法过程</h3><hr>
<p><img src="https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif"></p>
<ul>
<li>从数组中挑选出一个值,作为<code>基准值 k</code>.</li>
</ul>
<ul>
<li>重新排序序列,<strong>将所有小于<code>k</code>的值放到<code>k</code>前面,所有大于<code>k</code>的值放到<code>k</code>后面</strong>(也可以理解为将数组<code>a</code>切分为两个子数组<code>a[begin...k-1],a[k+1...end]</code>,其中前一个子数组都小于<code>k</code>,后一个子数组都大于<code>k</code>).</li>
</ul>
<ul>
<li>递归地将两个子数组进行快速排序(递归到最底部时,子数组的大小是零或一,也就是已经排序好了.).</li>
</ul>
<h3 id="划分函数"><a href="#划分函数" class="headerlink" title="划分函数"></a>划分函数</h3><hr>
<p><code>划分函数</code>就是上述步骤中的第二步,它将数组根据<code>基准值</code>进行重排序.根据<code>基准值</code>选择的位置不同,<code>划分函数</code>也有不同的实现方法,不过其根本思想都是将小于<code>基准值</code>的值放到前面,大于<code>基准值</code>的值放到后面.</p>
<h4 id="使用末尾元素作为基准值"><a href="#使用末尾元素作为基准值" class="headerlink" title="使用末尾元素作为基准值"></a>使用末尾元素作为基准值</h4><hr>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 使用末尾元素作为基准值来进行切分</span></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">partitionUseEnd</span><span class="params">(Comparable[] a, <span class="keyword">int</span> begin, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">    Comparable pivot = a[end]; <span class="comment">// 基准值,切分后的数组应满足左边都小于基准,右边都大于基准</span></span><br><span class="line">    <span class="keyword">int</span> i = begin - <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> j = begin; j &lt; end; j++) &#123;</span><br><span class="line">        <span class="comment">// 如果j小于基准值则与i交换</span></span><br><span class="line">        <span class="keyword">if</span> (less(a[j], pivot)) &#123;</span><br><span class="line">            i++;</span><br><span class="line">            swap(a, i, j);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="comment">// 将基准值交换到正确的位置上</span></span><br><span class="line">    <span class="keyword">int</span> pivotLocation = i + <span class="number">1</span>;</span><br><span class="line">    swap(a, pivotLocation, end);</span><br><span class="line">    <span class="keyword">return</span> pivotLocation;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="使用首元素作为基准值"><a href="#使用首元素作为基准值" class="headerlink" title="使用首元素作为基准值"></a>使用首元素作为基准值</h4><hr>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 使用首元素作为基准值来进行切分</span></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">partitionUseBegin</span><span class="params">(Comparable[] a, <span class="keyword">int</span> begin, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">    Comparable pivot = a[begin];</span><br><span class="line">    <span class="keyword">int</span> i = begin;</span><br><span class="line">    <span class="keyword">int</span> j = end + <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">while</span> (<span class="keyword">true</span>) &#123;</span><br><span class="line">        <span class="comment">// 从左向右扫描,直到找出一个大于等于基准的值</span></span><br><span class="line">        <span class="keyword">while</span> (less(a[++i], pivot)) &#123;</span><br><span class="line">            <span class="keyword">if</span> (i &gt;= end)</span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 从右向左扫描,直到找出一个小于等于基准的值</span></span><br><span class="line">        <span class="keyword">while</span> (less(pivot, a[--j])) &#123;</span><br><span class="line">            <span class="keyword">if</span> (j &lt;= begin)</span><br><span class="line">                <span class="keyword">break</span>;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        <span class="comment">// 如果指针i与j发生碰撞则结束循环</span></span><br><span class="line">        <span class="keyword">if</span> (i &gt;= j)</span><br><span class="line">            <span class="keyword">break</span>;</span><br><span class="line">        <span class="comment">// 将左边大于小于基准的值与右边小于等于基准的值进行交换</span></span><br><span class="line">        swap(a, i, j);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="comment">// 将基准值交换到正确的位置上</span></span><br><span class="line">    swap(a, begin, j);</span><br><span class="line">    <span class="keyword">return</span> j;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h3 id="代码实现"><a href="#代码实现" class="headerlink" title="代码实现"></a>代码实现</h3><hr>
<p>了解了<code>划分函数</code>的实现,剩下就只需要递归地调用<code>快速排序</code>不断地分解子任务即可.</p>
<p>注意,<code>快速排序</code>与<code>归并排序</code>不同,它不需要进行<code>归并</code>(划分后就已经是有序的了),并且是先进行<code>划分函数</code>,再分解任务.</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(Comparable[] a)</span> </span>&#123;</span><br><span class="line">    sort(a, <span class="number">0</span>, a.length - <span class="number">1</span>);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">private</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">sort</span><span class="params">(Comparable[] a, <span class="keyword">int</span> begin, <span class="keyword">int</span> end)</span> </span>&#123;</span><br><span class="line">    <span class="keyword">if</span> (begin &gt;= end)</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">int</span> k = partitionUseEnd(a, begin, end);</span><br><span class="line">    sort(a, begin, k - <span class="number">1</span>);</span><br><span class="line">    sort(a, k + <span class="number">1</span>, end);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
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<p>本文作者为<a target="_blank" rel="noopener" href="https://github.com/SylvanasSun/">SylvanasSun(sylvanassun_xtz@163.com)</a>,转载请务必指明原文链接.</p>
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